"Galton board" nuclear hyperpolarization

Abstract

We consider the problem of determining the spectrum of an electronic spin via polarization transfer to coupled nuclear spins and their subsequent readout. This suggests applications for employing dynamic nuclear polarization (DNP) for "ESR-via-NMR". In this paper, we describe the theoretical basis for this process by developing a model for the evolution dynamics of the coupled electron-nuclear system through a cascade of Landau-Zener anti-crossings (LZ-LACs). We develop a method to map these traversals to the operation of an equivalent "Galton board". Here, LZ-LAC points serve as analogues to Galton board "pegs", upon interacting with which the nuclear populations redistribute. The developed hyperpolarization then tracks the local electronic density of states. We show that this approach yields an intuitive and analytically tractable solution of the polarization transfer dynamics, including when DNP is carried out at the wing of a homogeneously broadened electronic spectral line. We apply this approach to a model system comprised of a Nitrogen Vacancy (NV) center electron in diamond, hyperfine coupled to N neighboring 13 C nuclear spins, and discuss applications for nuclear-spin interrogated NV center magnetometry. More broadly, the methodology of "one-to-many" electron-to-nuclear spectral mapping developed here suggests interesting applications in quantum memories and sensing, as well as wider applications in modeling DNP processes in the multiple nuclear spin limit.

Rapidly enhanced spin polarization injection in an optically pumped spin ratchet

“…Consider that the 𝑒-𝑛 Hamiltonian for 𝑁 nuclei (Fig. 1A) in the rotating frame at field 𝐵 0 has the form [44],…”

“…The first two terms denote the NV zero-field splitting (Δ=2.87GHz) and Zeeman field; Ω 𝑒 is the 𝑒-Rabi frequency (Ω 𝑒 =𝑐 𝑟 𝜂 𝑟 ) proportional to the MW power applied, and we assume an NV axis aligned with B 0 (along ẑ). The last term describes nuclear field in either electronic manifold -P 0 and P 1 are projection operators in the 𝑚 𝑠 =0 and 𝑚 𝑠 =1 manifolds, and the nuclear resonance frequencies herein are 𝜔 (0) 𝑗 and 𝜔 (1) 𝑗 respectively [44]:…”

“…, where 𝜔 𝑛 =𝛾 𝑛 𝐵 0 and A 𝑗 =𝐴 𝑗 ẑ+ 𝐴 ⊥ 𝑗 ⊥ is the hyperfine coupling. Spin ratchet polarization transfer is simplest to illustrate for a single 𝑒-𝑛 system [44,45]. Diagonalization leads to four Landau-Zener level anti-crossings (LZ-LACs), with energy gaps, 𝜀 1 ≈𝑐 𝑟 𝜂 𝑟 and 𝜀 2 ≈…”

“…Swept MWs cause a traversal through this LZ-LAC cascade. Its action can be evaluated under simplifying approximations that capture the experiments [44]: (i) LZ-LACs are assumed to be traversed sequentially, and, (ii) 𝑒-repolarization is assumed to occur at the start of every sweep event. This entails negligible laser action at the LZ-LACs, and is valid when B 𝜀 1,2 , as in our experiments.…”

“…1C). Hyperpolarization occurs when sweep rates 𝜔 𝑟 are such that T 1 →0 (adiabatic) and T 2 ≠0 (diabatic) [44]. The rate of polarization buildup is then ( [26]),…”